Belnap

Belnap is a surname associated with American philosopher and logician Nuel D. Belnap, known for work on the logic of information, truth, and paraconsistency.

He helped develop a four-valued logic, now often called Belnap-Dunn logic, to formalize how information can be true, false, both, or neither. In this logic, the four truth values are: true only, false only, both true and false, and neither true nor false. The logic is designed to tolerate inconsistency and incompleteness without trivial explosion, and is typically interpreted with a pair of orders: truth order and information order, forming a bilattice that underpins the semantics of the connectives.

The Belnap-Dunn logic is used in philosophy of logic and in computer science for knowledge representation and database theory, especially where data may be conflicting or incomplete. It provides a foundation for systems that can propagate partial or conflicting information and then be queried in a controlled way.

It also contributes to theories of truth, revision, and semantics where classical two-valued logic is inadequate.